{"abstract":"The exact restricted growth strings result violates the stated contract at new block choice inclusion.","category":"Numerics","checks":8,"contract":"Input length n (1..6), maximum blocks B>=1; return lexicographic restricted-growth strings a0=0, a_i<=1+max(prefix), using exactly B blocks.","evaluation_group":"s3-numerics-restricted-growth-strings","failed_approach":"The partial repair range(1,m+2) still violates the new block choice inclusion invariant.","family":"s3-numerics-restricted-growth-strings-new-block-choice-inclusion","id":"FA-15246","implementations":{"attempt":{"sha256":"abe433269e55c6fd988ab6b3ee0f2a8b1afe56c7cf3ede09b8d3bb14822e3c28","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    n,B=x;out=[]\n    def visit(prefix,m):\n     if len(prefix)==n:\n      if m+1==B:out.append(prefix)\n      return\n     for v in range(1,m+2):\n      if v>=B:continue\n      visit(prefix+[v],max(m,v))\n    visit([0],0)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 2], [[0, 1]]), ([2, 1], [[0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([1, 2], []), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([4, 1], [[0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([3, 3], [[0, 1, 2]]), ([5, 1], [[0, 0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]]), ([6, 3], [[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 2, 1], [0, 0, 0, 1, 2, 2], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 2], [0, 0, 1, 0, 2, 0], [0, 0, 1, 0, 2, 1], [0, 0, 1, 0, 2, 2], [0, 0, 1, 1, 0, 2], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 2, 1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 2, 0, 0], [0, 0, 1, 2, 0, 1], [0, 0, 1, 2, 0, 2], [0, 0, 1, 2, 1, 0], [0, 0, 1, 2, 1, 1], [0, 0, 1, 2, 1, 2], [0, 0, 1, 2, 2, 0], [0, 0, 1, 2, 2, 1], [0, 0, 1, 2, 2, 2], [0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 1, 2], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 2, 1], [0, 1, 0, 0, 2, 2], [0, 1, 0, 1, 0, 2], [0, 1, 0, 1, 1, 2], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 1, 2, 2], [0, 1, 0, 2, 0, 0], [0, 1, 0, 2, 0, 1], [0, 1, 0, 2, 0, 2], [0, 1, 0, 2, 1, 0], [0, 1, 0, 2, 1, 1], [0, 1, 0, 2, 1, 2], [0, 1, 0, 2, 2, 0], [0, 1, 0, 2, 2, 1], [0, 1, 0, 2, 2, 2], [0, 1, 1, 0, 0, 2], [0, 1, 1, 0, 1, 2], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 2, 1], [0, 1, 1, 0, 2, 2], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 2, 1], [0, 1, 1, 1, 2, 2], [0, 1, 1, 2, 0, 0], [0, 1, 1, 2, 0, 1], [0, 1, 1, 2, 0, 2], [0, 1, 1, 2, 1, 0], [0, 1, 1, 2, 1, 1], [0, 1, 1, 2, 1, 2], [0, 1, 1, 2, 2, 0], [0, 1, 1, 2, 2, 1], [0, 1, 1, 2, 2, 2], [0, 1, 2, 0, 0, 0], [0, 1, 2, 0, 0, 1], [0, 1, 2, 0, 0, 2], [0, 1, 2, 0, 1, 0], [0, 1, 2, 0, 1, 1], [0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 2, 0], [0, 1, 2, 0, 2, 1], [0, 1, 2, 0, 2, 2], [0, 1, 2, 1, 0, 0], [0, 1, 2, 1, 0, 1], [0, 1, 2, 1, 0, 2], [0, 1, 2, 1, 1, 0], [0, 1, 2, 1, 1, 1], [0, 1, 2, 1, 1, 2], [0, 1, 2, 1, 2, 0], [0, 1, 2, 1, 2, 1], [0, 1, 2, 1, 2, 2], [0, 1, 2, 2, 0, 0], [0, 1, 2, 2, 0, 1], [0, 1, 2, 2, 0, 2], [0, 1, 2, 2, 1, 0], [0, 1, 2, 2, 1, 1], [0, 1, 2, 2, 1, 2], [0, 1, 2, 2, 2, 0], [0, 1, 2, 2, 2, 1], [0, 1, 2, 2, 2, 2]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"3cbbb1e888d61b9fe41729657be94894d4b41949d94c21669037b56dc9d7c684","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    n,B=x;out=[]\n    def visit(prefix,m):\n     if len(prefix)==n:\n      if m+1==B:out.append(prefix)\n      return\n     for v in range(m+1):\n      if v>=B:continue\n      visit(prefix+[v],max(m,v))\n    visit([0],0)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 2], [[0, 1]]), ([2, 1], [[0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([1, 2], []), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([4, 1], [[0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([3, 3], [[0, 1, 2]]), ([5, 1], [[0, 0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]]), ([6, 3], [[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 2, 1], [0, 0, 0, 1, 2, 2], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 2], [0, 0, 1, 0, 2, 0], [0, 0, 1, 0, 2, 1], [0, 0, 1, 0, 2, 2], [0, 0, 1, 1, 0, 2], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 2, 1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 2, 0, 0], [0, 0, 1, 2, 0, 1], [0, 0, 1, 2, 0, 2], [0, 0, 1, 2, 1, 0], [0, 0, 1, 2, 1, 1], [0, 0, 1, 2, 1, 2], [0, 0, 1, 2, 2, 0], [0, 0, 1, 2, 2, 1], [0, 0, 1, 2, 2, 2], [0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 1, 2], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 2, 1], [0, 1, 0, 0, 2, 2], [0, 1, 0, 1, 0, 2], [0, 1, 0, 1, 1, 2], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 1, 2, 2], [0, 1, 0, 2, 0, 0], [0, 1, 0, 2, 0, 1], [0, 1, 0, 2, 0, 2], [0, 1, 0, 2, 1, 0], [0, 1, 0, 2, 1, 1], [0, 1, 0, 2, 1, 2], [0, 1, 0, 2, 2, 0], [0, 1, 0, 2, 2, 1], [0, 1, 0, 2, 2, 2], [0, 1, 1, 0, 0, 2], [0, 1, 1, 0, 1, 2], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 2, 1], [0, 1, 1, 0, 2, 2], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 2, 1], [0, 1, 1, 1, 2, 2], [0, 1, 1, 2, 0, 0], [0, 1, 1, 2, 0, 1], [0, 1, 1, 2, 0, 2], [0, 1, 1, 2, 1, 0], [0, 1, 1, 2, 1, 1], [0, 1, 1, 2, 1, 2], [0, 1, 1, 2, 2, 0], [0, 1, 1, 2, 2, 1], [0, 1, 1, 2, 2, 2], [0, 1, 2, 0, 0, 0], [0, 1, 2, 0, 0, 1], [0, 1, 2, 0, 0, 2], [0, 1, 2, 0, 1, 0], [0, 1, 2, 0, 1, 1], [0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 2, 0], [0, 1, 2, 0, 2, 1], [0, 1, 2, 0, 2, 2], [0, 1, 2, 1, 0, 0], [0, 1, 2, 1, 0, 1], [0, 1, 2, 1, 0, 2], [0, 1, 2, 1, 1, 0], [0, 1, 2, 1, 1, 1], [0, 1, 2, 1, 1, 2], [0, 1, 2, 1, 2, 0], [0, 1, 2, 1, 2, 1], [0, 1, 2, 1, 2, 2], [0, 1, 2, 2, 0, 0], [0, 1, 2, 2, 0, 1], [0, 1, 2, 2, 0, 2], [0, 1, 2, 2, 1, 0], [0, 1, 2, 2, 1, 1], [0, 1, 2, 2, 1, 2], [0, 1, 2, 2, 2, 0], [0, 1, 2, 2, 2, 1], [0, 1, 2, 2, 2, 2]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"45f91a036414b2e70e620afbf8ddccf67da101e1a6e0a69dbffeeacd83cd631e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    n,B=x;out=[]\n    def visit(prefix,m):\n     if len(prefix)==n:\n      if m+1==B:out.append(prefix)\n      return\n     for v in range(m+2):\n      if v>=B:continue\n      visit(prefix+[v],max(m,v))\n    visit([0],0)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 2], [[0, 1]]), ([2, 1], [[0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([1, 2], []), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([4, 1], [[0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([3, 3], [[0, 1, 2]]), ([5, 1], [[0, 0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]]), ([6, 3], [[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 2, 1], [0, 0, 0, 1, 2, 2], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 2], [0, 0, 1, 0, 2, 0], [0, 0, 1, 0, 2, 1], [0, 0, 1, 0, 2, 2], [0, 0, 1, 1, 0, 2], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 2, 1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 2, 0, 0], [0, 0, 1, 2, 0, 1], [0, 0, 1, 2, 0, 2], [0, 0, 1, 2, 1, 0], [0, 0, 1, 2, 1, 1], [0, 0, 1, 2, 1, 2], [0, 0, 1, 2, 2, 0], [0, 0, 1, 2, 2, 1], [0, 0, 1, 2, 2, 2], [0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 1, 2], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 2, 1], [0, 1, 0, 0, 2, 2], [0, 1, 0, 1, 0, 2], [0, 1, 0, 1, 1, 2], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 1, 2, 2], [0, 1, 0, 2, 0, 0], [0, 1, 0, 2, 0, 1], [0, 1, 0, 2, 0, 2], [0, 1, 0, 2, 1, 0], [0, 1, 0, 2, 1, 1], [0, 1, 0, 2, 1, 2], [0, 1, 0, 2, 2, 0], [0, 1, 0, 2, 2, 1], [0, 1, 0, 2, 2, 2], [0, 1, 1, 0, 0, 2], [0, 1, 1, 0, 1, 2], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 2, 1], [0, 1, 1, 0, 2, 2], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 2, 1], [0, 1, 1, 1, 2, 2], [0, 1, 1, 2, 0, 0], [0, 1, 1, 2, 0, 1], [0, 1, 1, 2, 0, 2], [0, 1, 1, 2, 1, 0], [0, 1, 1, 2, 1, 1], [0, 1, 1, 2, 1, 2], [0, 1, 1, 2, 2, 0], [0, 1, 1, 2, 2, 1], [0, 1, 1, 2, 2, 2], [0, 1, 2, 0, 0, 0], [0, 1, 2, 0, 0, 1], [0, 1, 2, 0, 0, 2], [0, 1, 2, 0, 1, 0], [0, 1, 2, 0, 1, 1], [0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 2, 0], [0, 1, 2, 0, 2, 1], [0, 1, 2, 0, 2, 2], [0, 1, 2, 1, 0, 0], [0, 1, 2, 1, 0, 1], [0, 1, 2, 1, 0, 2], [0, 1, 2, 1, 1, 0], [0, 1, 2, 1, 1, 1], [0, 1, 2, 1, 1, 2], [0, 1, 2, 1, 2, 0], [0, 1, 2, 1, 2, 1], [0, 1, 2, 1, 2, 2], [0, 1, 2, 2, 0, 0], [0, 1, 2, 2, 0, 1], [0, 1, 2, 2, 0, 2], [0, 1, 2, 2, 1, 0], [0, 1, 2, 2, 1, 1], [0, 1, 2, 2, 1, 2], [0, 1, 2, 2, 2, 0], [0, 1, 2, 2, 2, 1], [0, 1, 2, 2, 2, 2]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model. Inputs are restricted to the explicit contract; this is not a production algebra library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-numerics-restricted-growth-strings-new-block-choice-inclusion","generated_at":"2026-09-29T14:39:24.747760+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.","repair":"Use range(m+2) at the new block choice inclusion step.","root_cause":"The new block choice inclusion step uses range(m+1) instead of range(m+2).","sha256":"f16305b6b6811dff82ce3e628a767f3bdf6c352c1c9cd856f15e18ebf1d37627","title":"Restricted growth strings: new block choice inclusion · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.681,"exit_code":1,"observations":[{"actual":[[0,1]],"check":"explicit oracle 0","expected":[[0,1]],"passed":true},{"actual":[],"check":"explicit oracle 1","expected":[[0,0]],"passed":false},{"actual":[[0]],"check":"explicit oracle 2","expected":[[0]],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 5","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 6","expected":[[0,0,0]],"passed":false},{"actual":[[0,1,1]],"check":"explicit oracle 7","expected":[[0,0,1],[0,1,0],[0,1,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [], \"expected\": [[0, 0]], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [[0, 0, 0]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[0, 1, 1]], \"expected\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.159,"exit_code":1,"observations":[{"actual":[],"check":"explicit oracle 0","expected":[[0,1]],"passed":false},{"actual":[[0,0]],"check":"explicit oracle 1","expected":[[0,0]],"passed":true},{"actual":[[0]],"check":"explicit oracle 2","expected":[[0]],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 5","expected":[],"passed":true},{"actual":[[0,0,0]],"check":"explicit oracle 6","expected":[[0,0,0]],"passed":true},{"actual":[],"check":"explicit oracle 7","expected":[[0,0,1],[0,1,0],[0,1,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [], \"expected\": [[0, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [[0, 0, 0]], \"expected\": [[0, 0, 0]], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [], \"expected\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.134,"exit_code":0,"observations":[{"actual":[[0,1]],"check":"explicit oracle 0","expected":[[0,1]],"passed":true},{"actual":[[0,0]],"check":"explicit oracle 1","expected":[[0,0]],"passed":true},{"actual":[[0]],"check":"explicit oracle 2","expected":[[0]],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 5","expected":[],"passed":true},{"actual":[[0,0,0]],"check":"explicit oracle 6","expected":[[0,0,0]],"passed":true},{"actual":[[0,0,1],[0,1,0],[0,1,1]],"check":"explicit oracle 7","expected":[[0,0,1],[0,1,0],[0,1,1]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [[0, 0, 0]], \"expected\": [[0, 0, 0]], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"expected\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}